Algebra

Logarithmic Functions

Logarithmic Functions: Level 2 Challenges

         

Evaluate the following:

9log3(4) \Large 9^{\log_{3}(4)}

Do not use a calculator -- not even a slide rule!

log23×log34×log45××log127128=? \large \log_2 3 \times \log_3 4 \times \log_4 5 \times \cdots\times \log_{127} 128 = \, ?

True or false:

\quad \quad logx1=0\log_{x}1=0 for every x>0x>0.

cyclic(a,b,c)(11+logabc)=? \large \sum_{\text{cyclic}(a,b,c)} \left( \dfrac1{1 + \log_a bc} \right) = \, ?

Which of the options is correct about the number log418\log _{ 4 }{ 18 } ?

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